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Computer macroeconomic models for simulation experiments
COHPUTERMACROE3CONOMIC MODELS FOR SIMULATIOII RKPEFUMBB!PS MARTCHW A.A. end M.R. MOTZEV ') !f!hia paper diecuseeethe design of macroeconomiczlmodele in the form of a syetem of rrimultarreouz equations.A nev approachin thlo field is deecribed.The main idea ia that the eynthesieof the model ie based on a multi-stageselectionprocedure (MSSP).Characterietlcof thia procedureie that at each stage of selectionere generateda veriety of hypothesiseeabout the vented model. Each generatedhypothesis ie veriiied and eetimated,after which by inconclusivelimit choice of a given number, only few of them are selecteda~ "beet" in the I)enaeof a predefinedselection criteria.MSSP combinesin itself the principle of grouping of variables111, which lete to remove the coneequenceeof multicollinearityand und@reizedeamplee of data, the principleof externallyaddition "Crose veUdationw, which ie asymptoticequivalented with the Akaike'e criterionfor choiceof model 141 etc. Kesworde:eimultaneouaequationseysteme,multi-stageeelection prbcedure,macroeconomiceimulationmodele for Bulgariea economy, INTRODUCTION Thie paper representsa part of research done in the ecientifit laboratoryfor syeteme'enelg8isend managementin the Rlghere Institute of Economy "KarlMar~'~- Sofia. The main reault of this reset aruh la a detailedmethodologyfor automateddeeign of eimulatloamodels of economiceystemzwith a gred number of slgorythmaend prograrae organized in a few packet6 of annexedprogreum. MSSP FOR SYNTHESIZINGSIMULATIOHMODELS IN THE FORM OF SlMUJ2l!ANEoUS IQUATIONS In the MSSP which ia designedfor eynteeizingsimulationmodels in the form of a eyatem of eimulteneouaequation8(2X%)131,we CBP differentiatethree main parte: A. In the firat part, on the baeie of existingpracticalde ta, grouped in a table of obeervationeof researchedeyetem,we make a first choice of eigntiicantfactore,which will be includedin the model. Then: A.1, The generatingof the variety is done by includingnonlinear traneformationaend taking into account the pre-historyof the factore through eurietlc ccnrrideratione by the researcherand automw ticelly using a computerprogrem. A.11. Each competinghypothesisrepreeentea hypotheeieof inclusionor non-inolueionof en additionalfaotor in the table, that ia, a hypothesison the fact is this factor potentiallyimportantfor ')HighereInstituteof Economy "Karl Mamp - Sofia - Bulgmla
145
the mathematioal
deeeription
A.111, The limit
of choice
the reeearh
eyetem.
and the limiting
of
the variety
is do-
ne wring the criteria “correlation with a dependaut variableH, but can be supplemented with euristic 6olutione given by the researcher. In al.1 oaaee the preeervation of the initial factors - nprotection of the VW riables”
ie guaranteed.
B. The second part representa lection
of eaoh equation
wplzted equation
participating
ia not predetermined.
a procedure
for
in the model.
multi-stage
!Vhe form of
The tarrk of finding
eethe
the form and
coefficient6 of eaoh equation ie divided in many taak8 for determining the atefficfente of equation8 with two variablee - the principle of grouping of varfablee. Ia. this WV, we make certain of obtaining statistically important coeffioiente, based on a limited number of observations (undarsized samples of data), The form of the equation ie determined by a few conlrequitive stage of selection: B.I. The generation of the variety ie done by introducing neu intermidiate variable8 for each stage end the creation~of a new genera tion of lntermidiate equations function with two oeriablee which iuclude indirectly zuoreand more complex combin&ione of the initi&l faotora. B.11, Each generated equation la considered a6 potential desoription of a given connection in the model, which compete% with the other
poaeible
descriptions “fighting 8.11X, After es&% selection
for eurvival”. &age, there 18 no &&ice
of
a imi-
4ue equation, but a limit choice of a predetermined number of good equof non-finiliaed &olutlone, This gives atione ie done - the principle UE the possibility to obtain a set of alternative good equations. B.IV, !Che estimation of the ooeff’icient in each intermidiate equation ie &ne uring the criteria of the average square error. The existing set of data ie divided into two parts: a teaching set whiob is used for eetimating the ooefficient in the intermidiate equatione, and the control eet used for evelueing the adequacy of the obtained equatiof “Cro88 validation” choice of good model. ont3 - the principle B,V, T&e oboeen equation8 in a g&en generation are ueed for generating these
new, more complex equations
of
the next generation.
From
predetermined number ape chosen a8 good etc. B,VX. V!he selection procedure end.8 when certain conditions, Iimite or results are achieved, which the reeearoher want8 to obtain be eed on a given number of selections, achievement of an average minimum for the generation error and others. B.VII. At the end of the aeoond part of the MSSP automaticelly the full form of the beet equation8 is reetored. E8ah equation desori-
146
bing
a given connection in’ the model haa a given number of elteriu%tiVe va;rlations. C. In the third pert of the procedure from the obtalned equetione a ayntheeie of the eimulation model ie done in the form of SSB: C.I. The variety or alternative variants of the model, which represent
sic for
SSE is obtained by combined, already chosen, best C.11, Each of the competing hypothesleee repreeente incluelon
in the model of
a given
varlaat
equatiOna.
a hypothe-
of the separate
equ-
ation, C.111. Each generated SSE 18 considered au 8 potentia model which imitates the enalyzed eyetem. C.IV. The evaluation of theae competing model8 ie complexly done, using a great number of atatiatlcel ctiterim - coefficient of correlatlon, variation coefficient, average relative error, precisrrion in prognosis and othera. C,V. The final choice of the beet model ie made by the reeeercher, who haa the poeaibility to introduce some addition&l non-formalized considerations, but after having the guarantee of evalaeting a great number of possible models and the choice of a emall numbers of good one8. We have to remark, that in diiference to exietlng tradition&l method8 121, when the structural add parametrical identification of S&W la done eepacately, In the described MSSE’, thie ie done In a unified, highly automated procedure. In it, we have the poeeibilitp for impoeing predetermined Unite on SSE coefficienta aa in traditional methode, The diference ie that au additional structural identification is done daring multi-stage selection. During thie etructural identification automatically Borne of the variables are remov.ed and in the synt&j.zed model remain only thoeq which are important. In this way, aimultaneoualy the form of each equb tion ia determined aa well aa the important variable8 participating cmd a eetimatlon of the coefficient8 18 done. In addition the SSE coerficients can be obtained aa time fun* tione, which makes the MSSI? applicable to nonetationary eyetema, dezcribing
most economio SmuR-
proceaeee.
A FAMILY OF SIMUliATIOBMACRO-MODELS
IIogether with the design of a procedure for automated eyntheof simulation modola, we designed a family of aaaroeconomlo models called SIMUL The model8 from thle family oan be coluridered m a result end at the wme time M a baas for thie prooedure.
sis
147
Eaoh model from the SIMUR family ie deeignedwith a apeciaJ purpoee - experimentationand improvementof a given part of the MSSP for synthesisof SSE, The conclusionsobtainedfrom each experimentwith a model are used on one hand fox designingthe next model and on the other for improvingMSSP. In this way we achieveda parallel development and interactionbetween the family of model8 SIBfURand the MSSP for syntheaieof SSE. Short informationfor the SIMUR models is presentedin table 1.
r
lode1 Year of design)
Main purposes of design
Specific characteriatica
A one-productmacroeconomic model in the form of SSE wit: 5 equation%.Contains5 endo genous, 5 lag and 1 exogenouB variablegz-""~-----"II" I_______--"____________________-____1_1___11_3_p_____,
Analgeie of possibilitiesfor SIMUR-I automaticsynthesisof SSE 1978-1980)during the run of multi-stage aefection procedurea,
Design and experimentingof a Agregatedmacroeconomicmode programmingeystem for auto- iu the form of 12 interdepen SIMUR-II matic holding of simulation ding aimultaneouaequations, 1981-1982)experimentswith SSE.Analyeie Contains12 endogenoua,5 er of differentcriteriafor the ogenous and 3016~ variables ___________preoiefon'a eetimating of SSE ,_______ with 1% B___ of %L491z_s%%L._ ___..___________-___--_---_. It is being designed.Contat Improvingthe MSSP for synthesis of SSE with many equa- 39 equations,39 endogenoua, 7 exogenousand about tO0 lm, S~~-~~I tions, S~~~t~g and Pore1983-1985)casting of main maffueconomic variableswith a time lag OP up to 5 yere. indexes. CONCDUSIOIS 'Phi8paper preeente a new and perspectiveline in research and modellingof economicsyateme - ueing a multi-atageselectionprocedure data for sJmtheei8of simulationmodels. !Pheaccumulatedexperbazlta3. 1[1,3Tahows, that MSSP haa great advantagesover the existingmethodrrsystem dynamics,econometricapproach,egregatedmodellfng etc. In this conneotion,the presentedapproachha6 alarge field of applicationand needs further developmentin the followingmain direction@: A. Further design of algorythmsand progrmne for automated
elaborationof simulationmodels. B. The design of new simulationmacroeconomicmodels. In thie direction,special interestrepreeente the deeign of the mcslrro-models for differenteoci8liat cormtrieeusing the 88me set of veri8bles.Cn the basis of thie, it wif be possible to make valuable comparisonszmd 8nslysisof the common snd specific characteristics reflected in the differentmodels. LITERA'IURE Ivaahnenko,A. and J. Mtiller:Selbst-organisation von Vorhersage-modellen. VEElVerlag 'Iecbnik, Berlin, Verlsg Technika, Kiew, 1984. Malinvaud,E.: Methodes Statiatiquesde L'econometrie. Dunod, Parris,1969. Marchev, A. aad M.Motsev:SimulationMacroeconomicModels Deeigned in the Form of System8 of Simult8neous u&ions SyntheSi8:ing &ring the Run of Multi-etage Select Bfon Procedure.Scientificpapera of the Highere Instituteof EC+ nomy %.Harxf, ~01.1, Sofia 1983. of Choice Of Model Stone, PI.: &I AsymptOtiC.Ec@Vti~Ct# by Croes-Validationaad Akaike's CriterlOn.J.R.Statist. QOC. (1977)B39, 44-47.
149
145
the mathematioal
deeeription
A.111, The limit
of choice
the reeearh
eyetem.
and the limiting
of
the variety
is do-
ne wring the criteria “correlation with a dependaut variableH, but can be supplemented with euristic 6olutione given by the researcher. In al.1 oaaee the preeervation of the initial factors - nprotection of the VW riables”
ie guaranteed.
B. The second part representa lection
of eaoh equation
wplzted equation
participating
ia not predetermined.
a procedure
for
in the model.
multi-stage
!Vhe form of
The tarrk of finding
eethe
the form and
coefficient6 of eaoh equation ie divided in many taak8 for determining the atefficfente of equation8 with two variablee - the principle of grouping of varfablee. Ia. this WV, we make certain of obtaining statistically important coeffioiente, based on a limited number of observations (undarsized samples of data), The form of the equation ie determined by a few conlrequitive stage of selection: B.I. The generation of the variety ie done by introducing neu intermidiate variable8 for each stage end the creation~of a new genera tion of lntermidiate equations function with two oeriablee which iuclude indirectly zuoreand more complex combin&ione of the initi&l faotora. B.11, Each generated equation la considered a6 potential desoription of a given connection in the model, which compete% with the other
poaeible
descriptions “fighting 8.11X, After es&% selection
for eurvival”. &age, there 18 no &&ice
of
a imi-
4ue equation, but a limit choice of a predetermined number of good equof non-finiliaed &olutlone, This gives atione ie done - the principle UE the possibility to obtain a set of alternative good equations. B.IV, !Che estimation of the ooeff’icient in each intermidiate equation ie &ne uring the criteria of the average square error. The existing set of data ie divided into two parts: a teaching set whiob is used for eetimating the ooefficient in the intermidiate equatione, and the control eet used for evelueing the adequacy of the obtained equatiof “Cro88 validation” choice of good model. ont3 - the principle B,V, T&e oboeen equation8 in a g&en generation are ueed for generating these
new, more complex equations
of
the next generation.
From
predetermined number ape chosen a8 good etc. B,VX. V!he selection procedure end.8 when certain conditions, Iimite or results are achieved, which the reeearoher want8 to obtain be eed on a given number of selections, achievement of an average minimum for the generation error and others. B.VII. At the end of the aeoond part of the MSSP automaticelly the full form of the beet equation8 is reetored. E8ah equation desori-
146
bing
a given connection in’ the model haa a given number of elteriu%tiVe va;rlations. C. In the third pert of the procedure from the obtalned equetione a ayntheeie of the eimulation model ie done in the form of SSB: C.I. The variety or alternative variants of the model, which represent
sic for
SSE is obtained by combined, already chosen, best C.11, Each of the competing hypothesleee repreeente incluelon
in the model of
a given
varlaat
equatiOna.
a hypothe-
of the separate
equ-
ation, C.111. Each generated SSE 18 considered au 8 potentia model which imitates the enalyzed eyetem. C.IV. The evaluation of theae competing model8 ie complexly done, using a great number of atatiatlcel ctiterim - coefficient of correlatlon, variation coefficient, average relative error, precisrrion in prognosis and othera. C,V. The final choice of the beet model ie made by the reeeercher, who haa the poeaibility to introduce some addition&l non-formalized considerations, but after having the guarantee of evalaeting a great number of possible models and the choice of a emall numbers of good one8. We have to remark, that in diiference to exietlng tradition&l method8 121, when the structural add parametrical identification of S&W la done eepacately, In the described MSSE’, thie ie done In a unified, highly automated procedure. In it, we have the poeeibilitp for impoeing predetermined Unite on SSE coefficienta aa in traditional methode, The diference ie that au additional structural identification is done daring multi-stage selection. During thie etructural identification automatically Borne of the variables are remov.ed and in the synt&j.zed model remain only thoeq which are important. In this way, aimultaneoualy the form of each equb tion ia determined aa well aa the important variable8 participating cmd a eetimatlon of the coefficient8 18 done. In addition the SSE coerficients can be obtained aa time fun* tione, which makes the MSSI? applicable to nonetationary eyetema, dezcribing
most economio SmuR-
proceaeee.
A FAMILY OF SIMUliATIOBMACRO-MODELS
IIogether with the design of a procedure for automated eyntheof simulation modola, we designed a family of aaaroeconomlo models called SIMUL The model8 from thle family oan be coluridered m a result end at the wme time M a baas for thie prooedure.
sis
147
Eaoh model from the SIMUR family ie deeignedwith a apeciaJ purpoee - experimentationand improvementof a given part of the MSSP for synthesisof SSE, The conclusionsobtainedfrom each experimentwith a model are used on one hand fox designingthe next model and on the other for improvingMSSP. In this way we achieveda parallel development and interactionbetween the family of model8 SIBfURand the MSSP for syntheaieof SSE. Short informationfor the SIMUR models is presentedin table 1.
r
lode1 Year of design)
Main purposes of design
Specific characteriatica
A one-productmacroeconomic model in the form of SSE wit: 5 equation%.Contains5 endo genous, 5 lag and 1 exogenouB variablegz-""~-----"II" I_______--"____________________-____1_1___11_3_p_____,
Analgeie of possibilitiesfor SIMUR-I automaticsynthesisof SSE 1978-1980)during the run of multi-stage aefection procedurea,
Design and experimentingof a Agregatedmacroeconomicmode programmingeystem for auto- iu the form of 12 interdepen SIMUR-II matic holding of simulation ding aimultaneouaequations, 1981-1982)experimentswith SSE.Analyeie Contains12 endogenoua,5 er of differentcriteriafor the ogenous and 3016~ variables ___________preoiefon'a eetimating of SSE ,_______ with 1% B___ of %L491z_s%%L._ ___..___________-___--_---_. It is being designed.Contat Improvingthe MSSP for synthesis of SSE with many equa- 39 equations,39 endogenoua, 7 exogenousand about tO0 lm, S~~-~~I tions, S~~~t~g and Pore1983-1985)casting of main maffueconomic variableswith a time lag OP up to 5 yere. indexes. CONCDUSIOIS 'Phi8paper preeente a new and perspectiveline in research and modellingof economicsyateme - ueing a multi-atageselectionprocedure data for sJmtheei8of simulationmodels. !Pheaccumulatedexperbazlta3. 1[1,3Tahows, that MSSP haa great advantagesover the existingmethodrrsystem dynamics,econometricapproach,egregatedmodellfng etc. In this conneotion,the presentedapproachha6 alarge field of applicationand needs further developmentin the followingmain direction@: A. Further design of algorythmsand progrmne for automated
elaborationof simulationmodels. B. The design of new simulationmacroeconomicmodels. In thie direction,special interestrepreeente the deeign of the mcslrro-models for differenteoci8liat cormtrieeusing the 88me set of veri8bles.Cn the basis of thie, it wif be possible to make valuable comparisonszmd 8nslysisof the common snd specific characteristics reflected in the differentmodels. LITERA'IURE Ivaahnenko,A. and J. Mtiller:Selbst-organisation von Vorhersage-modellen. VEElVerlag 'Iecbnik, Berlin, Verlsg Technika, Kiew, 1984. Malinvaud,E.: Methodes Statiatiquesde L'econometrie. Dunod, Parris,1969. Marchev, A. aad M.Motsev:SimulationMacroeconomicModels Deeigned in the Form of System8 of Simult8neous u&ions SyntheSi8:ing &ring the Run of Multi-etage Select Bfon Procedure.Scientificpapera of the Highere Instituteof EC+ nomy %.Harxf, ~01.1, Sofia 1983. of Choice Of Model Stone, PI.: &I AsymptOtiC.Ec@Vti~Ct# by Croes-Validationaad Akaike's CriterlOn.J.R.Statist. QOC. (1977)B39, 44-47.
149